Isomorphic universality and the number of pairwise non-isomorphic models in the class of Banach spaces
نویسنده
چکیده
1 We develop the framework of natural spaces to study isomorphic embeddings of Banach spaces. We then use it to show that a sufficient failure of the generalized continuum hypothesis implies that the universality number of Banach spaces of a given density under a certain kind of positive embeddings (very positive embeddings), is high. An example of a very positive embedding is a positive onto embedding between C(K) and C(L) for 0-dimensional K and L such that the following requirement holds for all h 6= 0 and f ≥ 0 in C(K): if 0 ≤ Th ≤ Tf then there are constants a 6= 0 and b with 0 ≤ a · h+ b ≤ f and a · h+ b 6= 0.
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